A347076 Numbers m such that tau(m) = tau(m-1) + tau(m+1) and simultaneously sigma(m) = sigma(m-1) + sigma(m+1).

89484, 167784, 8587065618, 24033737496, 41249560520, 161721015522, 206958258156, 441151731162, 600656241732, 1013494535238, 4648478084262, 5099258875122, 7897343836494, 21060284613738, 26847208137084

Offset

1,1

Comments

Intersection of A073500 and A090502.

a(n) is even. If a(n) is odd then two consecutive numbers are perfect squares. This only happens with (0, 1) which does not give terms. - David A. Corneth, Aug 16 2021

Links

Table of n, a(n) for n=1..15.

Example

tau(89484) = tau(89483) + tau(89485); 12 = 4 + 8.
sigma(89484) = sigma(89483) + sigma(89485); 208824 = 91608 + 117216.

Mathematica

Select[Range[200000], DivisorSigma[{0, 1}, # - 1] + DivisorSigma[{0, 1}, # + 1] - DivisorSigma[{0, 1}, # ] == {0, 0} &] (* Amiram Eldar, Aug 16 2021 *)

Prog

(Magma) [m: m in [2..10^5] | #Divisors(m) eq #Divisors(m - 1) + #Divisors(m + 1) and &+Divisors(m) eq &+Divisors(m - 1) + &+Divisors(m + 1)]

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A073500, A090502.

Sequence in context: A184028 A209896 A255390 * A205290 A205898 A250452

Adjacent sequences: A347073 A347074 A347075 * A347077 A347078 A347079

Keyword

nonn,more

Author

Jaroslav Krizek, Aug 15 2021

Extensions

a(14)-a(15) from Martin Ehrenstein, Sep 24 2021

Status

approved